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Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

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Abstract

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.

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Abbreviations

MEMS:

micro-electro-mechanical-systems

t 1 :

film thickness

t 2 :

beam thickness

δ1 :

displacement of film

δ2 :

displacement of beam

ΔT :

temperature rise

α1 :

thermal expansion coefficient of film

α2 :

thermal expansion coefficient of beam

θ:

slope

ν:

deflection

σ x :

residual stress distribution

References

  • Behrens I, Doering L, Peiner E (2003) Piezoresistive cantilever as portable micro force calibration standard. J Micromech Microeng 13:S171–S177

    Article  Google Scholar 

  • Brissaud M, Sarah L, Gonnard P (2003) Modeling of a cantilever non-symmetric piezoelectric bimorph. J Micromech Microeng 13:832–844

    Article  Google Scholar 

  • Chen CT, Nguyen H, Wu MC (1999) A low voltage micromachined optical switch by stress-induced bending. Proc IEEE MEMS 1999:424–428

    Google Scholar 

  • Cho WI, Park NC, Yang H, Park YP (2002) Swing-arm-type PZT dual actuator with fast seeking for optical disk drive. Microsyst Technol 8:139–148

    Article  Google Scholar 

  • Cui T, Markus D, Zurn S, Polla DL (2004) Piezoelectric thin films formed by MOD on cantilever beams for micro sensors and actuators. Microsyst Technol 10:137–141

    Article  Google Scholar 

  • Ericson F, Greek S, Söderkvist J, Scheweitz JÅ (1997) High-sensitivity surface micromachined structures for internal stress and stress gradient evaluation. J Micromech Microeng 7:30–36

    Article  Google Scholar 

  • Fang W (1999) Determination of the elastic modulus of thin film materials using self-deformed micromachined cantilevers. J Micromech Microeng 9:230–235

    Article  Google Scholar 

  • Flinn PA, Gardner DS, Nix WD (1987) Measurement and interpretation of stress in a aluminum-based metallization as a function of thermal history. IEEE Transact Electron Device ED-34:689–698

    Article  Google Scholar 

  • Frühauf J, Gärtner E, Jänsch E (1999) Silicon as a plastic material. J Micromech Microeng 9:305–312

    Article  Google Scholar 

  • Helmbrecht MA, Srinivasan U, Rembe C, Howe RT, Muller RS (2001) Micromirrors for adaptive-optics arrays. Proc Transducers 2001:1290–1294

    Google Scholar 

  • Hodge TC, Bidstrup-Allen SA, Kohl PA (1997) Stresses in thin film metallization. IEEE Transact Compon Pack Manuf Technol A-20(2):241–248

    Article  Google Scholar 

  • Kobayashi T, Murakoshi Y, Maeda R (2004) Development of a novel self-sensitive atomic force microscope for nondestructive measurement of micro vertical surfaces. Microsyst Technol 10:423–425

    Article  Google Scholar 

  • Kuang Y, Huang QA, Lee NKS (2002) Numerical simulation of a polysilicon thermal flexure actuator. Microsyst Technol 8:17–21

    Article  Google Scholar 

  • Lee CY, Lee GB (2003) Micromachine-based humidity sensors with integrated temperature sensors for signal drift compensation. J Micromech Microeng 13:620–627

    Article  Google Scholar 

  • Lee GB, Lee HH, Chou TT (2003) An investigation of the residual stress in thin films under thermal process. Proc Nano Microsyst Conf 2003:113–117

    Google Scholar 

  • Lubecke VM, Barber B, Chan E, Lopez D, Goss ME, Gammel P (2001) Self-assembling MEMS variable and fixed RF inductors. J IEEE Transact Microwave Theory Tech 49(11):2093–2098

    Article  Google Scholar 

  • Pamula VK, Jog A, Fair RB (2001) Mechanical property measurement of thin-film gold using thermally actuated bimetallic cantilever beams. Proc Int Conf Model Simul Microsyst 2001:410–413

    Google Scholar 

  • Peng W, Bhushan B (2003) Transient analysis of sliding contact of layered elastic/plastic solids with rough surfaces. Microsyst Technol 9:340–345

    Article  Google Scholar 

  • Petronis S, Gold J, Kasemo B (2003) Microfabricated force-sensitive elastic substrates for investigation of mechanical cell-substrate interactions. J Micromech Microeng 13:900–913

    Article  Google Scholar 

  • Su Y, Evans AGR, Brunnschweiler AB, Ensell G (2002) Characterization of a highly sensitive ultra-thin piezoresistive silicon cantilever probe and its application in gas flow velocity sensing. J Micromech Microeng 12:780–785

    Article  Google Scholar 

  • Wu CT, Hsu W (2002) An electro-thermally driven microactuator with two dimensional motion. Microsyst Technol 8:47–50

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the financial support provided by the National Science Council in Taiwan (NSC 93-2218-E-212-011).

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, Da-Yeh University, Changhua, 515, Taiwan

    Chia-Yen Lee

  2. Department of Vehicle Engineering, National Pingtung University of Science and Technology, Pingtung, 912, Taiwan

    Chien-Hsiung Tsai, Li-Wen Chen & Yung-Chuan Chen

  3. Graduate Institute of Materials Engineering, National Pingtung University of Science and Technology, Pingtung, 912, Taiwan

    Lung-Ming Fu

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  1. Chia-Yen Lee
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  2. Chien-Hsiung Tsai
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  3. Li-Wen Chen
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  4. Lung-Ming Fu
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  5. Yung-Chuan Chen
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Correspondence to Yung-Chuan Chen.

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Lee, CY., Tsai, CH., Chen, LW. et al. Elastic–plastic modeling of heat-treated bimorph micro-cantilevers. Microsyst Technol 12, 979–986 (2006). https://doi.org/10.1007/s00542-006-0115-1

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  • DOI: https://doi.org/10.1007/s00542-006-0115-1

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